Delivery of MISAR Algorithms

Abstract : The two applications addressed in this report are: (1) spatial localization and scattering coefficient computation from the noisy echoes of chirp pulses interrogating a multiple point target environment, and (2) numerical deconvolution of Krueger's formula relating the reflectivity kernel p of a dielectric material to the echo resulting from the interaction of an orthogonally incident chirp pulse with the material. In parallel with these applications we develop several topics in the theory of the finite Zak transform (FZT). The FZT maps one-dimensional signals (vectors) on to two-dimensional signals (matrices). The Zak space representation provides a time-frequency image of the one-dimensional signal. Signal decomposition and processing such as convolution, matched filtering and the Fourier transform can be interpreted geometrically and computed by matrix operations in Zak space.